Simultaneous Untangling and Smoothing of Moving Mesh

In this paper a usefull technique for simultaneous untangling and smoothing of meshes is presented. It is based as an extension of an earlier smoothing strategy developed by the authors and employed to solve the computational mesh dynamics stage in fluid-structure interaction problems. In moving grid problems the mesh untangling is necessary to remedy the drawback produced by the elements inversion arisen from the boundary motion making the mesh invalid. The original smoothing strategy is defined in terms of the minimization of a functional associated with the mesh distortion employing an indicator of the element geometric quality. This functional becomes discontinuous when an element has null volume, making impossible to ob- tain a valid mesh from an invalid one. To circumvent this drawback, the original functional is transformed in order to guarantee its continuity for the whole space of volume values getting in this way the untangling technique. The regularization depends on one parameter, allowing to recover the original functional when this parameter tends to zero. This feature is very important because at first it is necessary to regularize the functional for making the untangling possible, i.e. to make the mesh valid, but then, it is advisable to use the original functional to make the smoothing optimal. This technique is applied to several test cases, including 2D and 3D meshes with simplicial elements. An additional example serves as a guide to show how this technique may be employed for mesh genera- tion too. [Submitted to Int J N Meth Engng (2006)]